That doesn't look like a cubic equation to me. If you multiply both sides by a3 you get a5+ 9a3+ 1= 0, a fifth degee equation. We can tell by "DesCartes' rule of signs" that it has no positive real root and only one negative real root. When a= 0, (0)5+ 9(0)+ 1= 1 which is positive and when a= -1/3, (-1/3)5+ 9(-1/3)+ 1= -2+ 1/243 which is negative. What does that tell you?

That doesn't look like a cubic equation to me. If you multiply both sides by a3 you get a5+ 9a3+ 1= 0, a fifth degee equation. We can tell by "DesCartes' rule of signs" that it has no positive real root and only one negative real root. When a= 0, (0)5+ 9(0)+ 1= 1 which is positive and when a= -1/3, (-1/3)5+ 9(-1/3)+ 1= -2+ 1/243 which is negative. What does that tell you?

Thanks, to solve it quickly i thought it as cubic overlooking the fact that it is actually a^-3, not a^3.